Answer :
To determine the perimeter of the right triangle with legs measuring 6 feet and 8 feet, we need to follow these steps:
1. Find the length of the hypotenuse:
The hypotenuse is the longest side of a right triangle, and it can be calculated using the Pythagorean theorem. The Pythagorean theorem states that for a right triangle with legs [tex]\(\text{a}\)[/tex] and [tex]\(\text{b}\)[/tex], and hypotenuse [tex]\(\text{c}\)[/tex], the relationship is given by:
[tex]\[ \text{c} = \sqrt{\text{a}^2 + \text{b}^2} \][/tex]
In this problem, [tex]\(\text{a} = 6\)[/tex] feet and [tex]\(\text{b} = 8\)[/tex] feet. Calculating the hypotenuse:
[tex]\[ \text{c} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ feet} \][/tex]
2. Calculate the perimeter:
The perimeter of a triangle is the sum of the lengths of its three sides. For our right triangle with leg lengths of 6 feet and 8 feet, and a hypotenuse of 10 feet, the perimeter is:
[tex]\[ \text{perimeter} = 6 \text{ feet} + 8 \text{ feet} + 10 \text{ feet} = 24 \text{ feet} \][/tex]
So, the perimeter of the triangle is:
[tex]\[ \text{24 feet} \][/tex]
Therefore, the correct answer is [tex]\( \boxed{24 \text{ feet}} \)[/tex].
1. Find the length of the hypotenuse:
The hypotenuse is the longest side of a right triangle, and it can be calculated using the Pythagorean theorem. The Pythagorean theorem states that for a right triangle with legs [tex]\(\text{a}\)[/tex] and [tex]\(\text{b}\)[/tex], and hypotenuse [tex]\(\text{c}\)[/tex], the relationship is given by:
[tex]\[ \text{c} = \sqrt{\text{a}^2 + \text{b}^2} \][/tex]
In this problem, [tex]\(\text{a} = 6\)[/tex] feet and [tex]\(\text{b} = 8\)[/tex] feet. Calculating the hypotenuse:
[tex]\[ \text{c} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ feet} \][/tex]
2. Calculate the perimeter:
The perimeter of a triangle is the sum of the lengths of its three sides. For our right triangle with leg lengths of 6 feet and 8 feet, and a hypotenuse of 10 feet, the perimeter is:
[tex]\[ \text{perimeter} = 6 \text{ feet} + 8 \text{ feet} + 10 \text{ feet} = 24 \text{ feet} \][/tex]
So, the perimeter of the triangle is:
[tex]\[ \text{24 feet} \][/tex]
Therefore, the correct answer is [tex]\( \boxed{24 \text{ feet}} \)[/tex].
